SOLUTION: Find an equation in standard form for the ellipse that satisfies the given conditions. Major axis endpoints ​(6​,6​) and ​(6​,-12​), minor axis length 4.

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Question 1134790: Find an equation in standard form for the ellipse that satisfies the given conditions.
Major axis endpoints ​(6​,6​) and ​(6​,-12​), minor axis length 4.

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

an equation in standard form for the ellipse is:

given:
major axis is
if endpoints ​(​,​) and ​(​,





minor axis length



Answer by ikleyn(52800)   (Show Source): You can put this solution on YOUR website!
.

            The solution by  @MathLover1  is   a b s o l u t e l y   w r o n g   and   t o t a l l y   i r r e l e v a n t.

            For your safety simply ignore it.

            I came to bring the correct solution - see below.


From the given information, the center of the ellipse is at the point (6,-3).



The major axis length is 6+12 = 18 units.

Hence, the major semi-axis is 18/2 = 9 units long.

The major axis is vertical, parallel to y-axis.


The minor axis is parallel to x-axis; the minor semi-axis has the length of 2.



At this point, we just can write the standard equation of the ellipse


     +  = 1.


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